Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x+4y &= 7 \\ 4x+3y &= 8\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $4x = -3y+8$ Divide both sides by $4$ to isolate $x$ $x = {-\dfrac{3}{4}y + 2}$ Substitute this expression for $x$ in the first equation. $2({-\dfrac{3}{4}y + 2}) + 4y = 7$ $-\dfrac{3}{2}y + 4 + 4y = 7$ Simplify by combining terms, then solve for $y$ $\dfrac{5}{2}y + 4 = 7$ $\dfrac{5}{2}y = 3$ $y = \dfrac{6}{5}$ Substitute $\dfrac{6}{5}$ for $y$ in the top equation. $2x+4( \dfrac{6}{5}) = 7$ $2x+\dfrac{24}{5} = 7$ $2x = \dfrac{11}{5}$ $x = \dfrac{11}{10}$ The solution is $\enspace x = \dfrac{11}{10}, \enspace y = \dfrac{6}{5}$.